There are fees for filing a personal injury lawsuit that a state or federal court mandates, but these fees are not terribly high. In some courts, the fee may be waived under special circumstances. Moreover, the majority of personal injury and wrongful death cases do not go to court; they are settled out of court instead. Settlements save money for the plaintiffs (the injured party) and help keep the court systems in the U.S. from being drowned in legal actions (a significant concern in our litigious society).
The greater cost would be for your legal representation. The attorney or law firm working on your behalf makes their living providing legal counsel, and they must charge in accord with their experience, knowledge, skills, and especially the amount of time that they devote to a case.
The good news is that nearly all personal injury lawyers work on a contingency-fee-basis, which means that the plaintiff doesn’t have to pay the lawyer’s or law firm’s fees until (or unless) the case is resolved through a settlement or a court verdict. Once a settlement or award is obtained, the lawyer or law firm typically takes a percentage of it to cover the costs of legal services.